Newtons method for multiple nonlinear equations

Again we use a Taylor series expansion to obtain Newton s method, representing the fth function in the vicinity of the current estimate as 

Assuming that is sufficiently close to the true solution Xs that we introduce little error by dropping the terms of quadratic and higher order, 

For convenience, we collect the first partial derivatives into the A x A Jacobian matrix jl l = with elements 

The truncated Taylor series expansion then becomes 

We thus generate the new estimate of the solution, Xs by solving the set of linear algebraic equations 

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